Research Papers

On the Comprehensive Kinematics Analysis of a Humanoid Parallel Ankle Mechanism

[+] Author and Article Information
Chengxu Zhou

Humanoid and Human Centered Mechatronics
Research Line,
Istituto Italiano di Tecnologia,
via Morego, 30,
Genova 16163, Italy
e-mail: zhouchengxu@gmail.com

Nikos Tsagarakis

Humanoid and Human Centered Mechatronics
Research Line,
Istituto Italiano di Tecnologia,
via Morego, 30,
Genova 16163, Italy
e-mail: nikos.tsagarakis@iit.it

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received October 23, 2017; final manuscript received June 25, 2018; published online August 6, 2018. Assoc. Editor: Pierre M. Larochelle.

J. Mechanisms Robotics 10(5), 051015 (Aug 06, 2018) (7 pages) Paper No: JMR-17-1358; doi: 10.1115/1.4040886 History: Received October 23, 2017; Revised June 25, 2018

In this paper, we present a thorough kinematics analysis of a humanoid two degrees-of-freedom (DoF) ankle module based on a parallel kinematics mechanism. Compared with the conventional serial configuration, the parallel kinematics ankle permits the distribution of the torque/power of the actuators to the two DoF of the ankle taking full advantage of available power/torque capacity of the two actuators. However, it complicates the kinematics study in return. In this work, a complete study of a parallel ankle mechanism is performed that permits the full characterization of the ankle module for the purpose of its design study, control, and performance evaluation. Screw theory is employed for mobility analysis to first determine the number and properties of the mechanism's DoFs. Then the inverse kinematics is solved analytically and the Jacobian matrix for describing the velocity relation between the ankle joints and motors is found. Based on these results, the forward kinematics of the parallel mechanism can be numerically computed using the Newton–Raphson method. The workspace of the ankle is also analyzed and the motor limits are decided accordingly. Finally, an experimental demonstration consisting of four tests is carried out to evaluate the proposed methods and ankle module.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Lenarcic, J. , and Stanisic, M. , 2003, “A Humanoid Shoulder Complex and the Humeral Pointing Kinematics,” IEEE Trans. Rob. Autom., 19(3), pp. 499–506. [CrossRef]
Carricato, M. , and Parenti-Castelli, V. , 2004, “A Novel Fully Decoupled 2-DOF Parallel Wrist,” Int. J. Rob. Res., 23(6), pp. 661–667. [CrossRef]
Morisawa, M. , Yakoh, T. , Murakami, T. , and Ohnishi, K. , 2000, “An Approach to Biped Robot With Parallel Mechanism,” International Workshop on Advanced Motion Control, Nagoya, Japan, Mar. 30–Apr. 1, pp. 537–541.
Sugahara, Y. , Endo, T. , Lim, H. , and Takanishi, A. , 2002, “Design of a Battery-Powered Multi-Purpose Bipedal Locomotor with Parallel Mechanism,” IEEE/RSJ International Conference on Intelligent Robots and Systems, 3, pp. 2658–2663.
Saglia, J. A. , Tsagarakis, N. G. , Dai, J. S. , and Caldwell, D. G. , 2009, “A High-Performance Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation,” Int. J. Rob. Res., 28(9), pp. 1216–1227. [CrossRef]
Roy, A. , Krebs, H. I. , Williams, D. J. , Bever, C. T. , Forrester, L. W. , Macko, R. M. , and Hogan, N. , 2009, “Robot-Aided Neurorehabilitation: A Novel Robot for Ankle Rehabilitation,” IEEE Trans. Rob., 25(3), pp. 569–582. [CrossRef]
Lohmeier, S. , Buschmann, T. , Schwienbacher, M. , Ulbrich, H. , and Pfeiffer, F. , 2006,“Leg Design for a Humanoid Walking Robot,” IEEE-RAS International Conference on Humanoid Robots, Genova, Italy, Dec. 4–6, pp. 536–541.
Hyon, S.-H. , Suewaka, D. , Torii, Y. , and Oku, N. , 2017, “Design and Experimental Evaluation of a Fast Torque-Controlled Hydraulic Humanoid Robot,” IEEE/ASME Trans. Mechatronics, 22(2), pp. 623–634. [CrossRef]
Feng, S. , Xinjilefu, X. , Atkeson, C. G. , and Kim, J. , 2015, “Optimization Based Controller Design and Implementation for the Atlas Robot in the Darpa Robotics Challenge Finals,” IEEE-RAS International Conference on Humanoid Robots, Seoul, South Korea, Nov. 3–5, pp. 1028–1035, pp. 1028–1035.
Kaminaga, H. , Ko, T. , Masumura, R. , Komagata, M. , Sato, S. , Yorita, S. , and Nakamura, Y. , 2016, “Mechanism and Control of Whole-Body Electro-Hydrostatic Actuator Driven Humanoid Robot Hydra,” International Symposium on Experimental Robotics, Tokyo, Japan, Oct. 3–6, pp. 656–665.
Knabe, C. , Griffin, R. , Burton, J. , Cantor-Cooke, G. , Dantanarayana, L. , Day, G. , Ebeling-Koning, O. , Hahn, E. , Hopkins, M. , Neal, J. , Jackson, N. , Chris, N. , Viktor, O. , John, P. , Michael, R. , John, S. , Yoonchang, S. , Jacob, W. , Nikolaus, W. , Jason, Z. , Alexander, L. , Brian, L. , and Tomonari, F. , 2017, “Team VALOR's ESCHER: A Novel Electromechanical Biped for the DARPA Robotics Challenge,” J. Field Rob., 34(5), pp. 912–939. [CrossRef]
Kakiuchi, Y. , Kamon, M. , Shimomura, N. , Yukizaki, S. , Takasugi, N. , Nozawa, S. , Okada, K. , and Inaba, M. , 2017, “Development of Life-Sized Humanoid Robot Platform With Robustness for Falling Down, Long Time Working and Error Occurrence,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada, Sept 24–28, pp. 689–696.
Reher, J. , Cousineau, E. A. , Hereid, A. , Hubicki, C. M. , and Ames, A. D. , 2016, “Realizing Dynamic and Efficient Bipedal Locomotion on the Humanoid Robot DURUS,” IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 16–21, pp. 1794–1801.
Mazumdar, A. , Spencer, S. J. , Hobart, C. , Salton, J. , Quigley, M. , Wu, T. , Bertrand, S. , Pratt, J. , and Buerger, S. P. , 2017, “Parallel Elastic Elements Improve Energy Efficiency on the STEPPR Bipedal Walking Robot,” IEEE/ASME Trans. Mechatronics, 22(2), pp. 898–908. [CrossRef]
Han, S. , Um, S. , and Kim, S. , 2016, “Mechanical Design of Robot Lower Body Based on Four-Bar Linkage Structure for Energy Efficient Bipedal Walking,” IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), Lausanne, Switzerland, Oct. 23–27, pp. 402–407.
Alfayad, S. , Ouezdou, F. B. , and Namoun, F. , 2009, “New Three DoF Ankle Mechanism for Humanoid Robotic Application: Modeling, Design and Realization,” IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 4969–4976.
Huang, Z. , and Li, Q. , 2003, “Type Synthesis of Symmetrical Lower-Mobility Parallel Mechanisms Using the Constraint-Synthesis Method,” Int. J. Rob. Res., 22(1), pp. 59–79.
Hunt, K. H. , 1978, Kinematic Geometry of Mechanisms, Oxford University Press, Oxford, UK.
Murray, R. M. , Li, Z. , Sastry, S. S. , and Sastry, S. S. , 1994, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.
Dai, J. S. , Huang, Z. , and Lipkin, H. , 2006, “Mobility of Overconstrained Parallel Mechanisms,” ASME J. Mech. Des., 128(1), pp. 220–229. [CrossRef]
Zhou, C. , Wang, X. , Li, Z. , and Tsagarakis, N. , 2017, “Overview of Gait Synthesis for the Humanoid COMAN,” J. Bionic Eng., 14(1), pp. 15–25. [CrossRef]
Zhou, C. , Fang, C. , Wang, X. , Li, Z. , and Tsagarakis, N. , 2016, “A Generic Optimization-Based Framework for Reactive Collision Avoidance in Bipedal Locomotion,” IEEE Conference on Automation Science and Engineering (CASE), Fort Worth, TX, Aug. 21–25, pp. 1026–1033.
Tsai, M.-S. , Shiau, T.-N. , Tsai, Y.-J. , and Chang, T.-H. , 2003, “Direct Kinematic Analysis of a 3-PRS Parallel Mechanism,” Mech. Mach. Theory, 38(1), pp. 71–83. [CrossRef]


Grahic Jump Location
Fig. 1

Mechanical model of the CogIMon humanoid robot (left) and close back view of its tibia without covers (right)

Grahic Jump Location
Fig. 2

The ankle's schematic representation

Grahic Jump Location
Fig. 3

Typical Control Framework for humanoid motion control. The superscript m indicates the variable is measured by the sensors.

Grahic Jump Location
Fig. 4

The ankle workspaces with respect to only the mechanism geometry, are illustrated in green for the default equal dimensions, in blue by increasing the motor bar length, in pink by increasing the rod length and in yellow by increasing the spacing between the two rods, respectively

Grahic Jump Location
Fig. 5

The workspace of the proposed ankle illustrated by different motor limits with the lower limit varying from −90 to −60 deg and the upper limit varying from 90 to 40 deg. The red box represents the desired workspace. Therefore, the minimum required motor limits are [−64, 50] degree.

Grahic Jump Location
Fig. 6

Ankle joint references for the four experimental tests

Grahic Jump Location
Fig. 7

Motor references solved by inverse kinematics for the four experimental tests

Grahic Jump Location
Fig. 8

Roll and pitch angle errors between the input references and the resultant ones after the IK-FK computation

Grahic Jump Location
Fig. 9

Number of iterations for solving the forward kinematics during experiment

Grahic Jump Location
Fig. 10

Computational time of inverse and forward kinematics during experiment

Grahic Jump Location
Fig. 11

Snapshots of the four experimental tests5



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In